Related papers: Distributional Results for Thresholding Estimators…

Evaluating predictive models is a crucial task in predictive analytics. This process is especially challenging with time series data where the observations show temporal dependencies. Several studies have analysed how different performance…

Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are…

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus…

The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…

For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with…

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…

We present methods for estimating loss-based measures of the performance of a prediction model in a target population that differs from the source population in which the model was developed, in settings where outcome and covariate data are…

When machine learning models are deployed on a test distribution different from the training distribution, they can perform poorly, but overestimate their performance. In this work, we aim to better estimate a model's performance under…

A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and…

We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…

Let $\{(X_i,Y_i)\}_{i\in \{1,..., n\}}$ be an i.i.d. sample from the random design regression model $Y=f(X)+\epsilon$ with $(X,Y)\in [0,1]\times [-M,M]$. In dealing with such a model, adaptation is naturally to be intended in terms of…

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…

We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time…

This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…

Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The…

We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis:…

In this paper we focus on the estimation of mutual information from finite samples $(\mathcal{X}\times\mathcal{Y})$. The main concern with estimations of mutual information is their robustness under the class of transformations for which it…

There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression…

We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…

We propose leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An…